The field of the invention relates to sampling and reconstruction of signals and images including MR images of multiple regions.
MR imaging is most commonly performed with 2D FT or 3D FT techniques, which require only a modest amount of prior knowledge about the object: 1) the object is assumed to be completely contained within a finite field of view (FOV); 2) the image is assumed to be band-limited in frequency space; i.e. its significant power spectrum does not extend beyond some maximum spatial frequency. If these two assumptions are valid, the usual sampling theorem (due to Whittaker, Kotel""nikov, and Shannon, or WKS, (1-4)) states that the image can be reconstructed by an inverse FT of a finite number of discrete samples of the image""s k-space representation. The spacing between the sampled k-space points is determined by the first assumption (the dimensions of the FOV), and the limits of the k-space sampling pattern are determined by the second assumption (the maximum spatial frequencies in the image). This method is widely used because: 1) it is based on relatively weak assumptions about the image, 2) it is relatively easy to acquire the Fourier-encoded signals stipulated by the WKS theorem, and 3) image reconstruction can be performed efficiently with a fast FT (FFT).
In contrast-enhanced carotid artery imaging, interventional imaging, functional imaging, cardiac imaging, and a number of other applications, the utility of MRI is limited by the speed with which the k-space data can be measured. Two general strategies have been used to shorten image acquisition time. 1) Gradient pulses with shorter rise times and/or larger amplitudes have been used in order to shorten the time required to gather a complete WKS data set. Unfortunately, gradient ramp rates and strengths are now approaching values at which neuromuscular stimulation can compromise patient safety and comfort. 2) More stringent assumptions can be made about the image in order to reduce the number of signals necessary to reconstruct it. Some of these xe2x80x9cconstrained imagingxe2x80x9d methods simply apply WKS sampling with stronger assumptions in order to increase the spacing between k-space points (reducing the FOV) or to reduce the k-space sampling limits (reducing image resolution). More novel approaches have utilized prior knowledge to express the image as a superposition of a small number of non-Fourier basis functions. The image""s projections onto these basis functions are computed from a reduced set of Fourier-encoded signals, or they are measured directly by performing non-Fourier encoding.
In this invention, we take a different approach. We generalize the WKS sampling theorem so that it can be applied to images which are supported on multiple regions within the FOV. By using this xe2x80x9cmultiple region MRxe2x80x9d (mrMR) sampling theorem, such images can be reconstructed from a fraction of the k-space samples required by the WKS theorem. Image reconstruction is performed with FFTs and without any noise amplification, just as in conventional FT MRI. In addition, we show how the method can be applied to a broader class of images having only their high contrast edges confined to known regions of the FOV. If this kind of prior knowledge is available, k-space can be sampled sparsely, and scan time can be reduced. The next section describes the theoretical framework of the mrMR approach. Then, the method is illustrated with simulated data and with experimental data from a phantom. Finally, we describe how the method was used to reduce the time of first-pass Gd-enhanced 3D carotid MRA so that it could be performed without bolus timing.
A method and apparatus are provided for transceiving a signal. The method includes the steps of transmitting a superposed frequency component of the signal within each of a plurality of non-adjacent frequency bands, using analogue or digital filters within a receiver to suppress all signals outside the plurality of frequency bands and to pass a filtered signal within the plurality of non-adjacent frequency bands, determining a set of substantially non-uniformly spaced times at which the filtered signal within the plurality of non-adjacent frequency bands should be sampled and sampling the filtered signal at the determined times to provide, sampled data. The method further includes the steps of Fourier transforming subsets of the sampled data, linearly combining the Fourier transformed subsets using a reconstruction matrix and extracting the signal from the linear combinations of the Fourier transformed subsets.
Traditional Fourier MR imaging utilizes the Whittaker-Kotel""nikov-Shannon (WKS) sampling theorem. This specifies the spatial frequency components which need be measured to reconstruct an image with a known field of view (FOV) and band-limited spatial-frequency contents. In this paper, we generalize this result in order to find the optimal k-space sampling for images that vanish except in multiple, possibly non-adjacent regions within the FOV. This provides the basis for xe2x80x9cmultiple region MRIxe2x80x9d (mrMRI), a method of producing such images from a fraction of the k-space samples required by the WKS theorem. Image reconstruction does not suffer from noise amplification and can be performed rapidly with fast Fourier transforms, just as in conventional FT MRI. The mrMRI method can also be used to reconstruct images that have low spatial-frequency components throughout the entire FOV and high spatial frequencies (i.e. edges) confined to multiple small regions. The greater efficiency of mrMR sampling can be parlayed into increased temporal or spatial resolution whenever the imaged objects have signal or xe2x80x9cedgexe2x80x9d intensity confined to multiple small portions of the FOV. Possible areas of application include MR angiography (MRA), interventional MRI, functional MRI, and spectroscopic MRI. The technique is demonstrated by using it to acquire Gd-enhanced first-pass 3D MRA images of the carotid arteries without the use of bolus-timing techniques.